An object will continue to be in the state of rest or in a state of motion unless an external force acts on it. The moment of inertia (I) is mostly specified based on the distribution of mass in the body with respect to the axis of rotation. The concept of inertia and momentum are regularly confused because of their similar definitions.

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• As the hollow sphere is uniform, the surface mass density (M/A) is constant.
• Calculate the initial recoil velocity of the rifle.
• Also calculate the magnitude of the force exerted by the wooden block on the bullet.
• As per the third law of motion, the force exerted by the insect on the car is equal and opposite to the force exerted by the car on the insect.
• When the resistance is offered by the body to continue to be in the uniform motion unless an external force acts on it.

A thin spherical shell of radius x, mass dm and thickness dx is taken as a mass element. Volume density (M/V) remains constant as the solid sphere is uniform. When the ball rolls on the flat surface of the ground, its motion is opposed by the force of friction (the friction arises between the ground and the ball).

Radius of Gyration

They collide and after the collision, the first object moves at a velocity of 1.67 ms–1. Let the mass of the plate be M and the radius be R. The centre is at O, and the axis is perpendicular to the plane of the plate. The mass element considered is a thin ring between x and x+dx with thickness dx and mass dm.

Moment of Inertia Formula

• This explains why it is difficult to rotate a wheel compared to a uniform disc.
• Moment of inertia from a Physics point of view is basically a quantitative measure of the rotational inertia or the angular mass of a body.
• As per the third law of motion, the nail exerts an equal and opposite force on the hammer.
• The mass element ‘dm’ considered is between x and x + dx from the origin.
• In these laws, the first law is also known as the Law of Inertia.

To know in detail about the inertia definition and the law of inertia, visit BYJU’S – The Learning App. Therefore, the moment of inertia of the system is 0.045kg m2. Therefore, the moment of inertia of the system is 0.087 kg m2. ⇒ The dimensional formula of the moment of inertia is given by, M1 L2 T0.
Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object. An object of mass 1 kg travelling in a straight line with a velocity of 10 ms–1 collides with, and sticks to, a stationary wooden block of mass 5 kg. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact.

How Did Galileo Explain Inertia?

The moment of inertia is usually specified with respect to a chosen axis of rotation. It mainly depends on the distribution of mass around an axis of rotation. Akhtar, Kiran, and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran started pondering over the situation. Akhtar said that since the motorcar was moving with a larger velocity, it exerted a larger force on the insect.

In this piece of article, let us discuss the first law of inertia in detail.Before discussing the law of inertia, let us know the Inertia Definition. Inertia is defined as a property of matter by which it remains at the state of rest or in uniform motion in the same straight line unless acted upon by some external force. A motorcar of mass 1200 kg is moving along a straight line with a uniform velocity of 90 km/h. Its velocity is slowed down to 18 km/h in 4 s by an unbalanced external %KEYWORD_VAR% force. Calculate the acceleration and change in momentum.

Which symbol is used to denote inertia?

The velocity of insect changes accordingly due to its mass as it is very small compared to the motorcar. Similarly, the velocity of motorcar is very insignificant because its mass is very large compared to the insect. A batsman hits a cricket ball which then rolls on a level ground. After covering a short distance, the ball comes to rest. The ball slows to a stop because (a) the batsman did not hit the ball hard enough.
Depending on the mass of the luggage and the magnitude of the force, the luggage may fall off the bus due to inertia. Tying up the luggage will secure its position and prevent it from falling off the bus. When a fireman holds a hose, which is ejecting large amounts of water at a high velocity, then a reaction force is exerted on him by the ejecting water in the backward direction. As a result of the backward force, the stability of the fireman decreases. Hence, it is difficult for him to remain stable while holding the hose.